Let L denote the discrete Dirac operator generated in 2 N, C 2 by the non-selfadjoint difference operators of first order a n+1 y (2) n+1 + b n y (2) n + p n y (1) n = λy (1) n a n−1 y (1) n−1 + b n y (1) n + q n y (2) n = λy (2) n , n ∈ N, (0.1) with boundary condition p k=0 y (2) 1 γ k + y (1) 0 β k λ k = 0, (0.2) where (a n), (b n), (p n) and (q n), n ∈ N are complex sequences, γ i , β i ∈ C, i = 0, 1, 2, ..., p and λ is a eigenparameter. We discuss the spectral properties of L and we investigate the properties of the spectrum and the principal vectors corresponding to the spectral singularities of L, if ∞ n=1 |n| |1 − a n | + |1 + b n | + p n + q n < ∞ holds